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Massive Neutrinos

by John G. Cramer

Alternate View Column AV-93
neutrino mass mu electron Super-Kamiokande underground Japanese
Published in the January-1999 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 06/28/98 and is copyrighted ©1998 by John G. Cramer.
All rights reserved. No part may be reproduced in any form without
the explicit permission of the author.

    This AV column is about recent evidence from the Super Kamiokande detector in Japan indicating that at least one of the three known neutrino flavors, the mu-neutrino, has a non-zero rest mass. To put this result in the proper context, I'll briefly review parts of the standard model of particle physics.

    The basic building blocks of the universe come in two particle types: half-integer spin "fermions" (spin = ½) and integer-spin "bosons" (spin = 0, 1, or 2). (For a discussion of these, see my AV column on Bose-Einstein condensation in the March-1996 issue of Analog.) The boson particles (gluon, Z°, W±, and photon) are "mediating particles" that create the forces (strong, weak, electromagnetic) that act between the fermion particles. Matter is therefore a collection of fermions held together by bosons.

    The spin ½ fermion particles in the standard model also come in two types: quarks and leptons. The six quarks (down, up, strange, charmed, bottom, top) have relatively large masses, fractional electric charges of ±1/3 or ±2/3, and respond to the strong interaction, the force that binds quarks into composite particles (protons, mesons, …) and also binds neutrons and protons to form nuclei.

    The six leptons do not respond to the strong interaction and come in two types. The three charged leptons (electron, mu, and tau, or e, m, and t) have charges of ±1, and rest masses of 0.511 MeV, 106 MeV, and 1,777 MeV, respectively. The three corresponding uncharged leptons are called neutrinos (ne, nm, and nt) and have rest masses that are known to be very small (or perhaps zero).

    In this column, we focus on the question of whether neutrinos have a non-zero rest mass. While there are good reasons to believe that gluons and photons have masses of exactly zero, there is no known reason why neutrinos should have exactly zero mass. If they do not, then they can engage in a peculiar behavior called "oscillation", in which they can switch identities as they travel. Consider, for example, two of the neutrino flavors, (e.g. nm and nt) that have the precisely the same spin (½) and the same charge (0) but differing rest masses. Can these two quantum states be distinguished on the basis external observations that do not include mass measurement? Answer: no, they cannot.

    When two quantum states cannot be distinguished, a peculiar thing happens; they mix to form two new states of matter that are distinguishable. In the case of two neutrino flavors, the mixing produces amplitudes for two states that are created together each time a neutrino is emitted. The two states have different rest masses and, for a given kinetic energy, travel with slightly different speeds. Because of the speed difference, they change their relative phasing along the path and interfere so as to cancel or reinforce depending on position. The result is an "oscillation" in which the emitted neutrino appears at some points along its path to be a pure mu-neutrino (nm) and at other points to be a pure tau-neutrino (nt). This is called a neutrino oscillation, and this is what the experimentalists at the Super Kamiokande detector in Japan appear to have observed.

    Historically, the original Kamiokande detector was built to search for an effect that has not been observed and may not exist: the decay of the proton. (See my Alternate View column on proton decay in the July-1984 issue of Analog.) In the early 1980s it was expected, on the basis of certain "grand-unified theories" (GUTs) fashionable at the time, that a proton might decay into lighter particles (e.g., e+ + p0) with a half-life of about 1032 years, a value short enough to be measurable. The Japanese built a large water-filled detector deep underground in a mine, seeking to observe such decays, and they have so far failed to do so (as have a number of other similar experiments around the world). The GUTs giving short half-life predictions for proton decay have now been falsified by experiment, and it is now clear that the proton half-life is 1033 years or more.

    However, the Japanese investment is the Kamiokande detector was saved by a cosmic accident, the arrival in February-1987 of light and neutrinos from the Large Magellanic Cloud, where an obscure star named Sanduleak -69o202 had exploded 160,000 years earlier to produce Supernova-1987A. (See my AV column in the December-1987 issue of Analog.) Kamiokande, which happened to be operating at the right time (several similar detectors were off-line then) detected 11 neutrino events from SN-1987A. This observation made a very important contribution to the brand new science of neutrino astrophysics.

    Based on this success, the Japanese and their American collaborators expanded the old detector with a larger volume of water and the addition of many new photomultiplier light-detectors. The new detector Super Kamiokande, is designed to detect neutrinos from the Sun, from supernovas, and from cosmic rays. Neutrinos interacting with the water are converted to charged particles (e or m leptons). These make Cerenkov light flashes that are recorded by the photomultipliers. The pattern and intensity of the detected light allows reconstruction of the energy and direction of the initial neutrino, and can distinguish electron-neutrinos (ne) from mu-neutrinos (nm). Super Kamiokande has now been operating for about a year and is beginning to produce results.

    One of the new results bears on an old puzzle which is called the cosmic ray neutrino discrepancy. The top of our atmosphere is continually bombarded with cosmic rays, particles (primarily protons, electrons, and gamma rays) having kinetic energies much larger than can be produced with the large accelerators at FermiLab and CERN. These particles hit the top of the atmosphere, producing a "shower" of multiple interactions as the primaries and their reaction products repeatedly collide with nitrogen and oxygen nuclei of the atmosphere. These energetic collisions produce a large number of charged pi-mesons (p±). The pi-meson, a combination of a quark and anti-quark in tight orbit, decays in its own rest frame in about 2 x 10-8 seconds to a mu-lepton (m) and a mu-neutrino (nm). The mu-lepton in turn decays in its own rest frame in about 2 x 10-6 seconds to an electron, an electron-neutrino (ne), and a mu-neutrino (nm). Therefore, the Earth's upper atmosphere is a source of energetic neutrinos, and there should be about two mu-neutrinos for every electron neutrino because of the p±®m±®e± decay chain. However, careful ground-based measurements of the ratio mu-neutrinos to electron neutrinos indicates that the ratio is about 1:1 rather than 2:1. Somehow, there are less mu-neutrinos than expected. This has been an unsolved astrophysics problem for many years.

    Now this puzzle appears to have been solved. The Super Kamiokande detector can observe neutrinos coming from the full sphere formed by the top of the Earth's atmosphere, from neutrinos produced directly overhead to those produced on the far side of the Earth. The far-side neutrinos must pass completely through the Earth to reach the detector, which is only possible because of the very small probability that neutrinos will interact with matter.

    Super Kamiokande sees that for electron-neutrinos, the probability of production is about the same for all points in the upper atmosphere. However, for mu-neutrinos a "disappearance effect" is observed. As the point of origin moves from the zenith directly overhead to the nadir (straight down), fewer and fewer mu-neutrinos reach the detector. The reduction factor depends directly on the increasing path length as the production point moves from zenith to nadir and the neutrinos have to travel farther and farther to the detector.

    The Super Kamiokande group interprets the increasing disappearance of mu-neutrinos with increasing path length as evidence for neutrino oscillations. Due to the oscillation process, the mu-neutrinos are transformed into some other flavor of neutrinos that is not detected. Since they do not see the electron-neutrinos increase as the mu-neutrinos disappear, they conclude that the oscillation is not between ne and nm. They consider two remaining possibilities: (1) an oscillation between nm and nt and (2) an oscillation between nm and hypothetical "sterile" neutrinos which have no interactions with matter.

    The Super Kamiokande detector also observed, with poorer statistics, neutrino interactions that produce p0 mesons in the detector. This "neutral-current" process should be equally strong for all three flavors of neutrinos (but zero for sterile neutrinos). It shows no evidence of oscillation behavior, making (1) is the more likely scenario. Therefore, the most plausible explanation of the new data is that nm and nt neutrinos have a very small mass difference, with a mass-squared difference Dm2 = 2.2 x 10-3 eV2. This mass difference is consistent with the observed oscillations.

    What are the implications of this observation? Massive neutrinos are one of the leading "hot dark matter" candidates, possible unobserved massive particles needed to explain several cosmology problems. Among these problems are the large-scale distribution of galaxies and galactic clusters and the high velocities of stars in galactic haloes. Also, Big Bang theorists would like to have a "critical" universe that is precisely balanced between the positive kinetic energy of Hubble expansion and the negative potential energy of gravitational attraction. Satisfying these conditions would require that the most massive of the neutrinos, probably the nt, to have mass around 1 eV, with the other neutrinos (ne and nm) having considerably smaller mass. Although the numbers are not yet completely pinned down, the Super Kamiokande results make a contribution to such a scenario.

    There is, of course, another neutrino problem. With solar neutrino detectors like Super Kamiokande we consistently detect only about 30% of the electron-neutrinos that we expect from fusion processes in the Sun. What does this new result have to say about the missing solar neutrinos? As mentioned above, electron-neutrinos show no evidence of disappearance or oscillation. This suggests that the mass difference between ne and nm is much smaller than between nm and nt.

    The current view is that the solar electron-neutrinos disappear by oscillating into mu-neutrinos due to the MSW effect, arising from the electron-neutrino's long passage through the matter of the solar interior on their way out. A neutrino mass spectrum in which the tau-neutrino had a mass of around .05 eV, the mu-neutrino had a mass of perhaps .005 eV, and the electron-neutrino had a mass of perhaps 10-5 eV would probably permit an explanation of both the cosmic-ray and the solar neutrino puzzles. However, a tau-neutrino mass of .05 eV is a rather low value for explaining the hot dark matter needed to make some cosmological models work.

    This leaves one remaining neutrino puzzle, the negative mass-squared values for the electron-neutrino that have been observed by six different studies of the end point of the tritium beta decay, as discussed in my previous Alternate View columns in the September-1992 and October-1993 issues of Analog. These results suggest the electron neutrino might have an imaginary mass with an absolute value of perhaps 12 eV (i.e., it might be a tachyon!).

    Has this possibility been eliminated by the new results? I don't think so. However, the tachyon neutrino hypothesis is sufficiently unpopular in the physics community that a neutrino mass spectrum with a tacyonic electron neutrino is not likely to be considered seriously as one of the alternatives, unless the new data forces attention in that direction.

    In any case, we know something this year that we did not know last year: neutrinos have mass. They are not zero-mass particles like the photon and the gluon. And they may represent at least a part of the dark matter that has been puzzling cosmologists and astrophysicists for the past decade.

John G. Cramer's 2016 nonfiction book (Amazon gives it 5 stars) describing his transactional interpretation of quantum mechanics, The Quantum Handshake - Entanglement, Nonlocality, and Transactions, (Springer, January-2016) is available online as a hardcover or eBook at: or

SF Novels by John Cramer: Printed editions of John's hard SF novels Twistor and Einstein's Bridge are available from Amazon at and His new novel, Fermi's Question may be coming soon.

Alternate View Columns Online: Electronic reprints of 212 or more "The Alternate View" columns by John G. Cramer published in Analog between 1984 and the present are currently available online at: .


"Evidence for oscillation of atmospheric neutrinos", The Super-Kamiokande Collaboration, Y. Fukuda, et al., submitted to Physics Letters, preprint hep-ex/9807003 in the LANL Archive, (July 3, 1998).

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